31 lines
920 B
Text
31 lines
920 B
Text
-- Copyright (c) 2014 Microsoft Corporation. All rights reserved.
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-- Released under Apache 2.0 license as described in the file LICENSE.
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-- Author: Jeremy Avigad, Jakob von Raumer
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-- Ported from Coq HoTT
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prelude
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import ..path ..equiv
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open eq
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-- Funext
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-- ------
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-- Define function extensionality as a type class
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-- structure funext [class] : Type :=
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-- (elim : Π (A : Type) (P : A → Type ) (f g : Π x, P x), is_equiv (@apD10 A P f g))
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-- set_option pp.universes true
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-- check @funext.mk
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-- check @funext.elim
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exit
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namespace funext
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attribute elim [instance]
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definition eq_of_homotopy [F : funext] {A : Type} {P : A → Type} {f g : Π x, P x} : f ∼ g → f = g :=
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is_equiv.inv (@apD10 A P f g)
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definition eq_of_homotopy2 [F : funext] {A B : Type} {P : A → B → Type}
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(f g : Πx y, P x y) : (Πx y, f x y = g x y) → f = g :=
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λ E, eq_of_homotopy (λx, eq_of_homotopy (E x))
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end funext
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